In-form City striker Max Caputo, 20, scored 83 seconds in and while brilliant Spanish playmaker Mata turned in one of his best performances yet, Victory couldn't overrun their crosstown rivals.
Teenage substitute Peter Antoniou, 18, fired home a second in the 56th minute, as City punished a toothless Victory - despite having just 10 shots to 21 - in the rematch of last season's grand final at AAMI Park.
The win came less than 72 hours after arriving back from City's Asian Champions League Elite win over Machida Zelvia in Japan.
"Incredible to be honest," Vidmar said.
"As everyone knows, the week that we've had has been pretty tough on everyone, but the character, the resilience that we showed this week, it's incredible.
"So full credit to the playing group. It hasn't been easy. We're up against a very good side tonight. They really pushed us, gave us everything, but we hung in there."
City's win came at a cost with full-back Nathaniel Atkinson (left hamstring) the latest to join their mounting injury list in the 12th minute.
City are conducting a review amid a second straight season affected by soft-tissue injuries, with Aziz Behich, Mathew Leckie, Elbasan Rashani, Medin Memeti and Samuel Souprayen all sidelined with hamstring strains.
City scored the fastest goal in Melbourne derby history when Andreas Kuen pinched the ball from Joshua Rawlins, then got the ball back from Zane Schreiber before slipping through Caputo, who beat Jack Duncan with a slick left-footed finish.
Caputo, 20, has scored four goals in his past four league matches and five in his past six overall.
After the goal, the Victory, led by Mata, dominated without taking their chances.
"We've got to be more efficient than that and better, that's the reality," coach Arthur Diles said.
"You've got to be better when you have that many chances, that many shots.
"You've got to execute better and that's the match in the end."
Mata forced a sharp save from new Socceroos call-up Patrick Beach in the sixth minute.
The Spaniard fizzed a left-footed strike mere inches wide of the top corner in the 21st minute and seven minutes later, squared the ball for Matt Grimaldi but the youngster fluffed the chance.
"He was great tonight," Diles said.
"Unfortunately, he wasn't rewarded for his great performance."
Victory had 10 shots (three on target) to City's three (two) in the first half and Mata let his frustration show.
Beach brilliantly batted away a wonderful bending strike from Grimaldi in the second half and was among the best players.
City struck again when Rawlins failed to clear a Mazzeo cross.
Kanamori took possession, sidestepped the Victory defender and slipped through Antoniou to fire home his first professional goal at the near post.
Victory midfielder Keegan Jelacic limped off with a knock in the 64th minute.
Mata fluffed a late chance, leaving the Victory to use the international break to lick their wounds.
